I'm struggling working in an environment that are using waterfall process. How people in my company usually process projects are CEO and other department managers come up ideas and tell directly to developers to code. There were no plan and no consideration of UX before I join. It turns out that there are a few users using our application. They have never taken user perspective when they plan but spend a lot of money to promote it. They believe they know our user and build it based on their assumption. So I thought if it takes Lean UX way to improve it, we can see actual use case scenarios and validate before developing it. The problem I have is the waterfall process has been used so long and it's hard to change the process to Lean UX. We even don’t have a dedicated product owner for it. If you have this situation, how and what do you start with?
Sounds like you have the same problem a lot of established companies have. Management don't really see the need for UX and proper processes. And so you have no budget for doing proper work.
My recommendation would be to find ways to prove to your managers about the value of proper UX methodology. You might want read the book "Undercover User Experience Design" if you haven't already done so. Lots of great tips there on how to do UX without a formal budget so you have results to demonstrate the importance of your methodologies.
On to your question of the first step: You have a hypothesis that the company's so call "subject matter experts" (SMEs) are too far removed from the actual users to provide good feedback about user requirements. Why don't you start by testing that assumption? Can you contact users of the system and perform some usability testing with them on the existing application? Failing that, people who are similar to your intended user groups might do. Ask them what's important to them when they think about the subject matter. Does this align with what your company SMEs tell you?
Prepare a presentation deck on your findings, a short video or audio snippets from actual testers would be nice to accompany your deck. Then just invite your managers for a meeting and off you go.